The differential migration of two planets due to planet-disk
interaction can result in capture into the 2:1
eccentricity-type resonances. Both the sequence of 2:1
eccentricity-type resonances that the system is driven
through by continued migration and the possibility of a
subsequent capture into the 4:2 inclination-type resonances
are sensitive to the migration rate within the range
expected for type II migration due to planet-disk
interaction. If the migration rate is fast, the resonant
pair can evolve into a family of 2:1 eccentricity-type
resonances different from those found by Lee (2004). This
new family has outer orbital eccentricity e2 \ga
0.4--0.5, asymmetric librations of both eccentricity-type
mean-motion resonance variables, and orbits that intersect
if they are exactly coplanar. Although this family exists
for an inner-to-outer planet mass ratio m1/m2 \ga
0.2, it is possible to evolve into this family by fast
migration only for m1/m2 \ga 2. Thommes & Lissauer
(2003) have found that a capture into the 4:2 inclination
resonances is possible only for m1/m2 \la 2. We show
that this capture is also possible for m1/m2 \ga 2
if the migration rate is slightly slower than that adopted
by Thommes & Lissauer. There is significant theoretical
uncertainty in both the sign and the magnitude of the net
effect of planet-disk interaction on the orbital
eccentricity of a planet. If the eccentricity is damped on a
timescale equal to or shorter than the migration timescale,
e2 may not be able to reach the values needed to enter
either the new 2:1 eccentricity resonances or the
inclination resonances for m1/m2 \ga 2. Thus, if
future observations were to reveal such a combination of
mass ratio and resonant configuration, it would place a
constraint on the strength of eccentricity damping during
migration, as well as on the rate of the migration itself.